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**Unformatted text preview: **Y ( z ) = A ( z ) X (-z ) i.e. only the alias term gets through? If yes, what condition needs to be satisfied for this to be true? 2 4. (Mitra, problem 13.40) Consider the system shown below. a) Show that the overall system is alias free, and calculate the transfer function ( ) ( ) ( ) Y z T z X z = in terms of H ( z ) and H 1 ( z ). b) What is T ( z ) if 2 2 1 1 1 ( ) [ ( ) ( )], ( ) [ ( ) ( )]. 2 2 H z H z H z H z z H z H z = +-=--c) If H ( z ) is a length 2 K filter, what are the lengths of the filters H ( z ) and H 1 ( z )? d) How many multiplies and adds are required to compute one output sample if the length of H ( z ) is 2 K samples?...

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